A device of the type mentioned in the introduction is disclosed, for example, by DE 103 08 975 B4. The known device has, for example, a thin film resonator in which the electrode layer, the piezoelectric layer and the further electrode layer are stacked one above the other in a stratified formation. The piezoelectric layer consists, for example, of zinc oxide. The upper electrode layer (top electrode) is made of gold and has the adsorption surface for adsorbing the substance of the fluid. The thin film resonator is applied to a silicon substrate via the lower electrode layer (bottom electrode). For acoustic decoupling of the silicon substrate and the thin film resonator from one another, an acoustic mirror made of λ/4-thick layers of different acoustic impedance, for example, is arranged between them.